Several of the nation's larger banks raised their prime lending rates again yesterday for the second time in 10 days, setting off another sharp drop in the stock market and heightening concerns about the prospect of a recession next year.

The boost was touched off by the First National Bank of Chicago and is the industry within a few days. It brought the prime rate to 11 precent, up from 10 3/4 percent before. The new level is the highest in more than 4 years.

The increase, which came partly in response to recent Federal Reserve Board credit tightening, sent shivers through the stock market. The Dow Jones industrial average plunged 15.08 points to 792.01 - its first dip below 800 since President Carter's dollar-rescue effort was announced Nov. 1.

However, Treasury Secretary W. Michael Blumenthal told a seminar in Cambridge, Mass., last night that "there is no recession in sight," despite glum predictions by nongovernment economists. He predicted the economy will grow next year at a respectable 3 per cent pace.

Blumenthal also forecast there will be no increase in unemployment in 1979 above the 6 percent level that has prevailed for the past several months. "We expect there might be some slipping," he said. But he asserted it would not be "significant."

Meanwhile, the Commerce Department reported that retail sales - key indicator of economic activity - fell during October for the first time in three months, dropping 0.5 percent following increases of 0.6 percent in September and 2.4 percent in August.

The dip was taken in some quarters as evidence that the economy was slowing further. However, William A. Cox, the department's deputy chief economist, said the decline was in line with earlier forecasts and does "not point to any conspicuous weakness" in the economy.

The figures came as key presidential inflation-fighter Barry Bosworth told an audience in Detroit he foresees a "pause" in the nation's economic expansion, with further credit tightening by the Federal Reserve if inflation does not abate.

Meanwhile, a top budget official here said the administration now expects oil-producing nations to raise crude oil prices by 10 percent later this year rather than the 5 percent or more that policy-makers had been predicting previously.

The official, Van Ooms, recently appointed chief economist at the office of Management and Budget, also conceded it would be "very hard" for the administration's inflation forecast to "hold up" if oil prices rose sharply and Iran stopped producting crude oil for export.

The White House has predicted that inflation will slow to between 6 and 6.5 percent next year, down from a 7 to 8 percent pace now. Most private economists, however, are forecasting the inflation rate will be 7 percent or more in 1979.

The rise in the prime rate was considered significant because most other key interest rates are pegged to the prime, which is the interest banks charge their most creditworthy corporate customers. The new 11 percent rate is the higest since July 1974.

The impact of recent interest-rate increases on construction was debated yesterday at a housing industry conference in Honolulu. Participants generally were optimistic that housing starts would remain high, but said all bets were off if the economy entered a recession.

The developments domestically were balanced by a relatively lackluster performance in the foreign exchange markets as the dollar held steady in major European and Asian trading centers. Gold prices, however, rose by as much as $2 an ounce.

The move by the First National Bank of Chicago in raising the prime rate was joined almost immediately by Harris Trust and Savings Bank and the First Pennsylvania Bank of Philadelphia. First National City Bank of New York is expected to announce a prime rate raise later.